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Natural Deduction for NonClassical Logics
, 1996
"... We present a framework for machine implementation of families of nonclassical logics with Kripkestyle semantics. We decompose a logic into two interacting parts, each a natural deduction system: a base logic of labelled formulae, and a theory of labels characterizing the properties of the Kripke m ..."
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Cited by 11 (3 self)
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We present a framework for machine implementation of families of nonclassical logics with Kripkestyle semantics. We decompose a logic into two interacting parts, each a natural deduction system: a base logic of labelled formulae, and a theory of labels characterizing the properties of the Kripke models. By appropriate combinations we capture both partial and complete fragments of large families of nonclassical logics such as modal, relevance, and intuitionistic logics. Our approach is modular and supports uniform proofs of correctness and proof normalization. We have implemented our work in the Isabelle Logical Framework.
Philosophical ìntuitions' and scepticism about judgement
 Dialectica
, 2004
"... 1. What are called ‘intuitions ’ in philosophy are just applications of our ordinary capacities for judgement. We think of them as intuitions when a special kind of scepticism about those capacities is salient. 2. Like scepticism about perception, scepticism about judgement pressures us into conceiv ..."
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Cited by 10 (1 self)
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1. What are called ‘intuitions ’ in philosophy are just applications of our ordinary capacities for judgement. We think of them as intuitions when a special kind of scepticism about those capacities is salient. 2. Like scepticism about perception, scepticism about judgement pressures us into conceiving our evidence as facts about our internal psychological states: here, facts about our conscious inclinations to make judgements about some topic rather than facts about the topic itself. But the pressure should be resisted, for it rests on bad epistemology: specifically, on an impossible ideal of unproblematically identifiable evidence. 3. Our resistance to scepticism about judgement is not simply epistemic conservativism, for we resist it on behalf of others as well as ourselves. A reason is needed for thinking that beliefs tend to be true. 4. Evolutionary explanations of the tendency assume what they should explain. Explanations that appeal to constraints on the determination of reference are more promising. Davidson’s truthmaximizing principle of charity is examined but rejected. 5. An alternative principle is defended on which the nature of reference is to maximize knowledge rather than truth. It is related to an externalist conception of mind on which knowing is the central mental state. 6. The knowledgemaximizing
12 On What Grounds What
"... Substance is the subject of our inquiry; for the principles and the causes we are seeking are those of substances. For if the universe is of the nature of a whole, substance is its first part;... —Aristotle(1984: 1688; Meta.1069a18–20) On the now dominant Quinean view, metaphysics is about what ther ..."
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Cited by 10 (0 self)
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Substance is the subject of our inquiry; for the principles and the causes we are seeking are those of substances. For if the universe is of the nature of a whole, substance is its first part;... —Aristotle(1984: 1688; Meta.1069a18–20) On the now dominant Quinean view, metaphysics is about what there is. Metaphysics so conceived is concerned with such questions as whether properties exist, whether meanings exist, and whether numbers exist. I will argue for the revival of a more traditional Aristotelian view, on which metaphysics is about what grounds what. Metaphysics so revived does not bother asking whether properties, meanings, and numbers exist. Of course they do! The question is whether or not they are fundamental. In §1 I will distinguish three conceptions of metaphysical structure. In §2 I will defend the Aristotelian view, coupled with a permissive line on existence. In §3 I will further develop a neoAristotelian framework, built around primitive grounding relations.
Validity concepts in prooftheoretic semantics
 ProofTheoretic Semantics. Special issue of Synthese
"... Abstract. The standard approach to what I call “prooftheoretic semantics”, which is mainly due to Dummett and Prawitz, attempts to give a semantics of proofs by defining what counts as a valid proof. After a discussion of the general aims of prooftheoretic semantics, this paper investigates in det ..."
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Cited by 5 (4 self)
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Abstract. The standard approach to what I call “prooftheoretic semantics”, which is mainly due to Dummett and Prawitz, attempts to give a semantics of proofs by defining what counts as a valid proof. After a discussion of the general aims of prooftheoretic semantics, this paper investigates in detail various notions of prooftheoretic validity and offers certain improvements of the definitions given by Prawitz. Particular emphasis is placed on the relationship between semantic validity concepts and validity concepts used in normalization theory. It is argued that these two sorts of concepts must be kept strictly apart. 1. Introduction: Prooftheoretic
Description PHIL 478: Philosophical Logic Fall Semester, 2006
"... The course will study selected extensions of and alternatives to classical propositional logic. The extensions include modal, conditional, and tense logics; the alternatives include intuitionistic, many valued, and relevance logics. In each case, we will consider the philosophical issues raised by t ..."
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The course will study selected extensions of and alternatives to classical propositional logic. The extensions include modal, conditional, and tense logics; the alternatives include intuitionistic, many valued, and relevance logics. In each case, we will consider the philosophical issues raised by these logics, though most of our time will be devoted to becoming familiar with the logics themselves, from both a semantic and a prooftheoretic standpoint. Throughout the course, we will trade depth for breadth; the goal is not to study any of these logics in mathematical detail, but just to get a sense of the range of possibilities. Time and place
Concepts and Axioms
, 1998
"... The paper discusses the transition from informal concepts to mathematically precise notions; examples are given, and in some detail the case of lawless sequences, a concept of intuitionistic mathematics, is discussed. A final section comments on philosophical discussions concerning intuitionistic lo ..."
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The paper discusses the transition from informal concepts to mathematically precise notions; examples are given, and in some detail the case of lawless sequences, a concept of intuitionistic mathematics, is discussed. A final section comments on philosophical discussions concerning intuitionistic logic in connection with a "theory of meaning". What I have to tell here is not a new story, and it does not contain any really new ideas. The main difference with my earlier discussions of the same topics ([TD88, chapter16],[Tro91]) is in the emphasis. This paper starts with some examples of the transition from informal concepts to mathematically precise notions, followed by a more detailed discussion of one of these examples, the intuitionistic notion of a choice sequence, arguing for the lasting interest of this notion for the philosophy of mathematics. In a final section, I describe my own position relative to some of the philosophical discussions concerning intuitionistic logic in the wr...
Understanding Intuitionism
, 1997
"... This paper is an attempt to understand the differences between them. I am grateful to Mitsuru Yasuhara for stimulating discussions of this material and for pinpointing errors and obscurities in earlier drafts. I also wish to thank Simon Kochen and Per MartinLof for helpful comments. ..."
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This paper is an attempt to understand the differences between them. I am grateful to Mitsuru Yasuhara for stimulating discussions of this material and for pinpointing errors and obscurities in earlier drafts. I also wish to thank Simon Kochen and Per MartinLof for helpful comments.
Objective Subjectivity: Allocentric and Egocentric Representation in Thought and Experience
, 2000
"... this dissertation I address both questions of application and questions of constitution. The primary aim of this chapter is to begin by addressing the question of what it means for judgments to be objective or subjective. One common use of the notions of objectivity and subjectivity is to demarcate ..."
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this dissertation I address both questions of application and questions of constitution. The primary aim of this chapter is to begin by addressing the question of what it means for judgments to be objective or subjective. One common use of the notions of objectivity and subjectivity is to demarcate kinds of judgment (or thought or belief). On such a usage, prototypically objective judgments concern matters of empirical and mathematical fact such as the moon has no atmosphere and two and two are four. In contrast, prototypically subjective judgments concern matters of value and preference such as Mozart is better than Bach and vanilla ice cream with ketchup is disgusting. I offer these examples not to take sides on whether such judgments actually are objective or subjective, but only to call attention to a typical way of using "objective" and "subjective". The question arises as to what it means in this context to call these respective judgments "objective" and "subjective". Some have proposed that the difference hinges on truth. Objective judgments are absolutely true, whereas the truth of subjective judgments is relative to the person making the judgment: my judgments are true for me, your judgments are true for you. You and I can each utter "vanilla tastes great" but in your mouth this may constitute a truth and in my mouth it may constitute a falsehood. Subjective judgments are subject relative. Some philosophers have noted an analogy between this kind of subject relativity and a kind that obtains for indexical expressions. You and I can both utter "I am here" and thereby express different propositions. Some philosophers have construed indexicality as an instance of subjectivity and some others have even gone so far as to argue that subjectivity just is indexicality....